I was in Beijing earlier this week, attending a conference on Sino-American relations. The conference was jointly sponsored by Beijing University and Harvard, and featured a number of prominent Chinese and American academics (and a few former policymakers). Our Chinese hosts were exceptionally welcoming, and the absence of clean air didn't prevent the other participants from making lots of interesting presentations. (For another summary of the proceedings, check out Alan Alexandroff's account here).

The panel on which I spoke was focused on how the United States and China could cooperate to enhance international security. I made five basic points and thought I'd pass them along to you.

1.Positive and Negative Forms of Security Cooperation. In theory (I argued), there are two broad forms that Sino-American security cooperation could take. The first type consists of positive acts of collaboration, such as counterterrorism measures or anti-piracy operations (as in the Gulf of Aden). One can also imagine more ambitious sorts of cooperation, as when the two states jointly approve U.N. Security Council sanctions against Iran. One could even imagine situations where China and the United States might join forces to halt some deep civil conflict, although that is obviously less likely.

The second type of security cooperation is essentially negative: Each side seeks to enhance its mutual security by limiting or restraining its activities in some important realm. Traditional arms control is an obvious example of this sort of cooperation, as was the U.S.-Soviet "Incidents at Sea" agreement. Sino-American agreement on a naval "code of conduct" or a ban on cyberattacks would be of this type as well.

In short, it is not hard to think of various ways that Washington and Beijing could cooperate to reduce the risk of international conflict. But is significant cooperation likely, and what factors might make it more or less probable?

2. Prospects for Cooperation. Unfortunately, the probability that two states will engage in significant acts of security cooperation -- and especially of the positive sort noted above -- is largely determined by the level of amity or trust between them. If they have generally positive relations, cooperation is fairly easy. If there is a lot of mutual suspicion, however, positive acts of cooperation will be hard to sustain because both sides may fear that the other is gaining some sort of advantage. Paradoxically: Security cooperation is easiest when it is least important and hardest when it would be most valuable. Welcome to the wonderful world of international relations!

3. Rival Grand Strategies. The main barrier to extensive Sino-American cooperation to enhance global security is the tension between their respective grand strategies. China's central strategic aim is to continue to grow economically, gradually acquire greater economic and military power, and eventually reduce or eliminate the U.S. security role in Asia. Not by conquest or force necessarily, but by co-opting or cowing neighboring states into distancing themselves from the United States. The reason is easy to fathom: Just as U.S. leaders wanted to expel the European great powers from the Western Hemisphere (see under: Monroe Doctrine), China's leaders believe they will be more secure in the long run if the United States does not have a large military presence near their borders and does not have close security ties with their neighbors.

The United States, by contrast, wants to stay in Asia in order to keep China from establishing a dominant position there. Since the U.S. became a great power, a core principle of its grand strategy was to prevent any single power from dominating either Europe or Asia. That's why the United States opposed Germany in World War I, fought Germany and Japan in World War II, and worked to contain the Soviet Union in the Cold War. If no single power dominates Europe or Asia, the states there will worry mostly about each other, and none are able to focus solely on the United States or do much to interfere over in the Western Hemisphere. Accordingly, the U.S. will want to stay in Asia, to backstop its allies there and prevent Beijing from dominating the region.

4. Will the U.S. and China Act with Restraint?If the United States and China each pursue their respective grand strategies energetically, conflicts of interest will be numerous and intense, and we will see lots of trouble down the road. In this sort of world, there won't be much security cooperation between the two sides, and there will be a very intense security competition in Asia itself, with each side trying to cultivate allies of its own and trying simultaneously to undermine the opposing coalition. But if the two states pursue their strategies in a restrained, even lazy, fashion, they'll find it easier to reach common ground on some issues and might even engage in positive acts of collaboration on occasion.

Alas, I don't think the latter outcome is likely. Restraint is not something the United States does very well, and the recent "pivot" to Asia is probably a harbinger of more to come. Fiscal constraints will put some limits on what the United States can do, but you can bet that the Pentagon sees a coming conflict with China as a major force driver and will push hard for an assertive approach and the preservation of our current "forward presence." Similarly, China's own level of restraint has declined as its relative power has grown, and Deng Xiaoping's strategy of the "peaceful rise" has been gradually giving way to a more assertive nationalism. If China's economic growth rate does not slow significantly, I wouldn't expect a lot of restraint on either side. (FWIW, I think a slowdown is nearly inevitable, which will create big problems for the Chinese leadership but might dampen tensions somewhat.)

5. Stability for the Long Term. Unfortunately, managing Sino-American relations over the long term will be even harder. If Chinese leaders are consistently smart, judicious, farsighted, clear-eyed, and wise, and if their American counterparts consistently exhibit similar qualities, then the two governments may be able to manage their future relations without serious trouble. But the history of both countries suggests that there is very little chance that these idyllic circumstances will prevail every year for the next several decades. Sooner or later, we are bound to get a cadre of foolish, impetuous, or incompetent leaders in one capital or the other, or maybe even both at the same time. If "wise leadership" is the prerequisite for managing Sino-American rivalry over the long haul, in short, history suggests one ought to worry. A lot.

The bottom line is that Washington and Beijing have an obvious interest in taking steps now that might make their relationship easier to manage in the future. In particular, establishing rules of the road for naval activity (similar to the earlier Incidents at Sea agreement) might reduce the danger of an unintended clash on the high seas. Reaching an understanding on the use of unmanned drones or cyberattacks would help too. Military-to-military contacts and other forms of elite exchange would be a good idea as well, so that elites in both societies know the people with whom they are dealing personally and are less likely to misread or misinterpret what they may do while in official positions. None of these steps makes rivalry disappear, but together they could help keep it from boiling over.

And that just might be the greatest contribution that these two states could make to international peace and security over the next 25 years.